A downlink cooperative non-orthogonal multiple access (NOMA) multiuser underwater wireless optical communication (UWOC) system with a greedy scheduling scheme has been proposed for the Internet of Underwater Things. In particular, the near user plays as a relay to assist the far user, and both decode-and-forward and amplify-and-forward relaying protocols are considered. Relying on the Gauss-Laguerre quadrature formula, the analytical expressions for the outage probability of users are derived considering the degrading effects of the underwater channel, namely, absorption, scattering, and turbulence-induced fading. The outage performance is further analyzed systematically under different water types, targeted data rates, the number of users, the receiver aperture size, and the power allocation coefficient. Numerical results demonstrate that the performance of the far user can be improved by the proposed cooperative NOMA technology. Moreover, the proposed cooperative NOMA system performs better compared with both conventional OMA and non-cooperative NOMA systems. Monte Carlo simulation results are presented to confirm the accuracy of derived expressions, which have a tight agreement with analytical results.